Finite multiple zeta values and finite Euler sums
J Zhao - arXiv preprint arXiv:1507.04917, 2015 - arxiv.org
arXiv preprint arXiv:1507.04917, 2015•arxiv.org
The alternating multiple harmonic sums are partial sums of the infinite series defining the
Euler sums which are the alternating version of the multiple zeta value series. In this paper,
we present some systematic structural results of the van Hamme type congruences of these
sums, collected as finite Euler sums. Moreover, we relate this to the structure of the Euler
sums, which generalizes the corresponding result of the multiple zeta values. We also
provide a few conjectures with extensive numerical support.
Euler sums which are the alternating version of the multiple zeta value series. In this paper,
we present some systematic structural results of the van Hamme type congruences of these
sums, collected as finite Euler sums. Moreover, we relate this to the structure of the Euler
sums, which generalizes the corresponding result of the multiple zeta values. We also
provide a few conjectures with extensive numerical support.
The alternating multiple harmonic sums are partial sums of the infinite series defining the Euler sums which are the alternating version of the multiple zeta value series. In this paper, we present some systematic structural results of the van Hamme type congruences of these sums, collected as finite Euler sums. Moreover, we relate this to the structure of the Euler sums, which generalizes the corresponding result of the multiple zeta values. We also provide a few conjectures with extensive numerical support.
arxiv.org